Geodesic
A new formulation of the Stokes problem in a cylinder, and its spectral discretization
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 5, pp. 781-810

Voir la notice de l'article provenant de la source Numdam

We analyze a new formulation of the Stokes equations in three-dimensional axisymmetric geometries, relying on Fourier expansion with respect to the angular variable: the problem for each Fourier coefficient is two-dimensional and has six scalar unknowns, corresponding to the vector potential and the vorticity. A spectral discretization is built on this formulation, which leads to an exactly divergence-free discrete velocity. We prove optimal error estimates.

DOI : 10.1051/m2an:2004039
Classification : 65N35
Keywords: Stokes problem, spectral methods, axisymmetric geometries 
@article{M2AN_2004__38_5_781_0,
     author = {Abdellatif, Nehla and Bernardi, Christine},
     title = {A new formulation of the {Stokes} problem in a cylinder, and its spectral discretization},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {781--810},
     publisher = {EDP-Sciences},
     volume = {38},
     number = {5},
     year = {2004},
     doi = {10.1051/m2an:2004039},
     mrnumber = {2104429},
     zbl = {1079.76055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004039/}
}
TY  - JOUR
AU  - Abdellatif, Nehla
AU  - Bernardi, Christine
TI  - A new formulation of the Stokes problem in a cylinder, and its spectral discretization
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2004
SP  - 781
EP  - 810
VL  - 38
IS  - 5
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004039/
DO  - 10.1051/m2an:2004039
LA  - en
ID  - M2AN_2004__38_5_781_0
ER  - 
%0 Journal Article
%A Abdellatif, Nehla
%A Bernardi, Christine
%T A new formulation of the Stokes problem in a cylinder, and its spectral discretization
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2004
%P 781-810
%V 38
%N 5
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2004039/
%R 10.1051/m2an:2004039
%G en
%F M2AN_2004__38_5_781_0
Abdellatif, Nehla; Bernardi, Christine. A new formulation of the Stokes problem in a cylinder, and its spectral discretization. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 38 (2004) no. 5, pp. 781-810. doi: 10.1051/m2an:2004039

Cité par Sources :